Download App

Transformation Formulae — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsTransformation Formulae1 Mark
MCQ
$\text{If}\ \sin2\theta+\sin2\phi=\frac{1}{2}\ \text{and}\ \cos2\theta\\ \ +\cos2\phi=\frac{3}{2},\text{then}\cos^2(\theta-\phi)=$
  • A
    $\frac{3}{8}$
  • ✓
    $\frac{5}{8}$
  • C
    $\frac{3}{4}$
  • D
    $\frac{5}{4}$
✓

Answer

Correct option: B.
$\frac{5}{8}$
Given:
$\sin2\theta+\sin2\phi=\frac{1}{2}....(\text{i})$
and
$\cos2\theta+\cos2\phi=\frac{3}{2}....(\text{ii})$
Squaring and adding (i) and (ii), we get:
$(\sin2\theta+\sin2\phi)^2+(\cos2\theta+\cos2\phi)^2=\frac{1}{4}+\frac{9}{4}$
$\Rightarrow\ \Big[2\sin\Big(\frac{2\theta+2\phi}{2}\Big)\cos\Big(\frac{2\theta-2\phi}{2}\Big)\Big]^2\\ \ \ \ \ +\Big[2\cos\Big(\frac{2\theta+2\phi}{2}\Big)\cos\Big(\frac{2\theta-2\phi}{2}\Big)\Big]^2=\frac{5}{2}$
$\Rightarrow\ 4\sin^2(\theta+\phi)\cos^2(\theta-\phi)\\ \ \ +4\cos^2(\theta+\phi)\cos^2(\theta-\phi)=\frac{5}{2}$
$\Rightarrow\ 4\cos^2(\theta-\phi)[\sin^2(\theta+\phi)+\cos^2(\theta+\phi)]=\frac{5}{2}$
$\Rightarrow\ 4\cos^2(\theta-\phi)=\frac{5}{2}$
$\Rightarrow\ \cos^2(\theta-\phi)=\frac{5}{8}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Transformation Formulae→Transformation Formulae — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Choose the correct answers from the given four option:
If $A$ and $B$ are two sets, then $\text{A} \cap (\text{A} \cup \text{B})$ equals.
→
$a{x^2} + 2{y^2} + 2bxy + 2x - y + c = 0$ represents a circle through the origin, if
→
Let $S$ be a set containing n elements and we select $2$ subsets $A$ and $B$ of $S$ at random then the probability that $A \cup B = S$ and $A \cap B = \phi $ is
→
If $f(9) = 9$, $f'(9) = 4$, then $\mathop {\lim }\limits_{x \to 9} \frac{{\sqrt {f(x)} - 3}}{{\sqrt x - 3}} = $
→
A box contains $25$ tickets numbered $1, 2, ....... 25$. If two tickets are drawn at random then the probability that the product of their numbers is even, is
→
If A lies in second quadrant $3\tan\text{A}+4=0,$ then the value of $2\cot\text{A}-5\cot\text{A}+\sin\text{A}$ is:
→
An ellipse and a hyperbola have the same centre origin, the same foci and the minor-axis of the one is the same as the conjugate axis of the other. If $ e_1, e_2 $ be their eccentricities respectively, then  $e_1^{ - 2} + e_2^{ - 2}$ equals
→
Let $C$ be the locus of the mirror image of a point on the parabola $y ^{2}=4 x$ with respect to the line $y = x$. Then the equation of tangent to $C$ at $P (2,1)$ is :
→
If the roots of the given equation $(\cos p - 1){x^2} + (\cos p)x + \sin p = 0$ are real, then
→
${ }^{(2 n+1)} C_0-{ }^{(2 n+1)} C_1+{ }^{(2 n+1)} C_2-\ldots .{ }^{2 n+1} C_{2 n}=$
→